All Courses
Get the App Signup / Login
Sign in Open App
Mathematics Exam  >  Mathematics Tests  >  Topic-wise Tests & Solved Examples for Mathematics  >  Differential Equations - 21 - Mathematics MCQ

Differential Equations - 21 - Mathematics MCQ


Test Description

20 Questions MCQ Test Topic-wise Tests & Solved Examples for Mathematics - Differential Equations - 21

Differential Equations - 21 for Mathematics 2024 is part of Topic-wise Tests & Solved Examples for Mathematics preparation. The Differential Equations - 21 questions and answers have been prepared according to the Mathematics exam syllabus.The Differential Equations - 21 MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Differential Equations - 21 below.
Solutions of Differential Equations - 21 questions in English are available as part of our Topic-wise Tests & Solved Examples for Mathematics for Mathematics & Differential Equations - 21 solutions in Hindi for Topic-wise Tests & Solved Examples for Mathematics course. Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free. Attempt Differential Equations - 21 | 20 questions in 60 minutes | Mock test for Mathematics preparation | Free important questions MCQ to study Topic-wise Tests & Solved Examples for Mathematics for Mathematics Exam | Download free PDF with solutions
Differential Equations - 21 - Question 1
Save

The particular integral of the differential eauation (D2 - 4)y  = sin 4x is given by

Detailed Solution for Differential Equations - 21 - Question 1

Proof : The required particular integral is given by

Differential Equations - 21 - Question 2
Save

The particular integral of the differential equation (D2 + 9)y = cos 2x + sin 2x is given by

Detailed Solution for Differential Equations - 21 - Question 2

Proof : Th required particular integral is given by

1 Crore+ students have signed up on EduRev. Have you? Download the App
Differential Equations - 21 - Question 3
Save

The general solution of the differential equation 

Detailed Solution for Differential Equations - 21 - Question 3

The given differential equation is
  ....(i)
Corresponding homogeneous differential equation is
 ....(ii)
The general solution of (i) is given by
y = complementary' function + A particular solution of (i)
or y = General solution of (ii) + A particular solution of (i)
General solution of (ii).
Auxiliary equation is given by 



∴  Required general solution of (i) is given by

Differential Equations - 21 - Question 4
Save

The particular integral of the differential equation is given by
Detailed Solution for Differential Equations - 21 - Question 4

The given differential equation is
f(D)y = xex,
where f(D) = D2 + 2D + 5
The required Particular Integral is given by


Differential Equations - 21 - Question 5
Save

The particular integral of the differential equation  sin 2x is given by
Differential Equations - 21 - Question 6
Save

The particular integral of the differential equation (D2 - 2D + 1)y = xex sin x is given by
Detailed Solution for Differential Equations - 21 - Question 6

The required Particular Integral is given by 

(Note : Im denotes imaginary part of the bracketed quantity)

Differential Equations - 21 - Question 7
Save

Detailed Solution for Differential Equations - 21 - Question 7

Differential Equations - 21 - Question 8
Save

A differential equation of the type  where a1, a2, ..., an are constants and X is either a constant or a function of x, is also called
Detailed Solution for Differential Equations - 21 - Question 8

This equation is known as Cauchy Euler equation.

Differential Equations - 21 - Question 9
Save

The differential equation  can be tranformed into a linear differential equation with constant coefficients by means of the substitution
Detailed Solution for Differential Equations - 21 - Question 9

Proof : The given differential equation is

Now consider the transformation 

   ...(iii)


and so on
Finally we substitute for

into equation (i) and get a differential equation with constant coefficients with y as dependent variable and z as independent variable.

Differential Equations - 21 - Question 10
Save

Which one of the following differential equations is equivalent to the differential equation 
Detailed Solution for Differential Equations - 21 - Question 10

Hint : Substitute z = log x and using equation (iii) and (iv), we get

Differential Equations - 21 - Question 11
Save

The initial value problem dy/dx = x, y(0) = 1 has
Detailed Solution for Differential Equations - 21 - Question 11


Differential Equations - 21 - Question 12
Save

The initial value problem 
Differential Equations - 21 - Question 13
Save

Which of the following differential equations is exact
Differential Equations - 21 - Question 14
Save

The first integral of the differential equation  where P0, P1, P2 and P3 are functions of x, is given by
Differential Equations - 21 - Question 15
Save

The first integral of the differential equation 
Differential Equations - 21 - Question 16
Save

The first integral of the differential equation 
Differential Equations - 21 - Question 17
Save

The differential equation 2ydx - (3y - 2x) dy = 0 is
Detailed Solution for Differential Equations - 21 - Question 17



Differential Equations - 21 - Question 18
Save

The general solution of the differential equation (x + y - 3)dx - (2x + 2y + 1)dy = 0 is
Detailed Solution for Differential Equations - 21 - Question 18


  ......(i)

Differential Equations - 21 - Question 19
Save

The general solution of the differential equation 
Detailed Solution for Differential Equations - 21 - Question 19



 so differential equation (1) is exact
so its solution is

Differential Equations - 21 - Question 20
Save

The solution of the differential equation y (2x + y2)dx + x(x + 3y2)dy = 0, is
Detailed Solution for Differential Equations - 21 - Question 20


27 docs|150 tests
Join Course
Information about Differential Equations - 21 Page
In this test you can find the Exam questions for Differential Equations - 21 solved & explained in the simplest way possible. Besides giving Questions and answers for Differential Equations - 21, EduRev gives you an ample number of Online tests for practice
Download as PDF

Important Questions for Differential Equations - 21

Find all the important questions for Differential Equations - 21 at EduRev.Get fully prepared for Differential Equations - 21 with EduRev's comprehensive question bank and test resources. Our platform offers a diverse range of question papers covering various topics within the Differential Equations - 21 syllabus. Whether you need to review specific subjects or assess your overall readiness, EduRev has you covered. The questions are designed to challenge you and help you gain confidence in tackling the actual exam. Maximize your chances of success by utilizing EduRev's extensive collection of Differential Equations - 21 resources.

Differential Equations - 21 MCQs with Answers

Prepare for the Differential Equations - 21 within the Mathematics exam with comprehensive MCQs and answers at EduRev. Our platform offers a wide range of practice papers, question papers, and mock tests to familiarize you with the exam pattern and syllabus. Access the best books, study materials, and notes curated by toppers to enhance your preparation. Stay updated with the exam date and receive expert preparation tips and paper analysis. Visit EduRev's official website today and access a wealth of videos and coaching resources to excel in your exam.

Online Tests for Differential Equations - 21 Topic-wise Tests & Solved Examples for Mathematics

Practice with a wide array of question papers that follow the exam pattern and syllabus. Our platform offers a user-friendly interface, allowing you to track your progress and identify areas for improvement. Access detailed solutions and explanations for each test to enhance your understanding of concepts. With EduRev's Online Tests, you can build confidence, boost your performance, and ace Differential Equations - 21 with ease. Join thousands of successful students who have benefited from our trusted online resources.
© EduRev
Education Revolution
Follow Us
Signup to see your scores go up
within 7 days!
Takes less than 10 seconds to signup